Numerical Analysis for the Nonlinear Free Vibration of Shallow Shells
Publication: Journal of Engineering Mechanics
Volume 128, Issue 12
Abstract
A variational approach for the nonlinear free vibration of shallow shells having a quadrilateral boundary is presented in this paper. Natural coordinates ξ and η are used to map the prescribed geometry in the plane. Displacement fields corresponding to u, w, and are expressed in terms of the product of two algebraic functions, the form of which is so chosen that the displacement boundary condition can be imposed by manipulating the coefficients. In arriving at the stiffness matrix, no simplification is applied to the nonlinear strains and the variation of the complete energy equation is considered. For the plate problems numerical results are obtained and compared with approximate analytical results by other researchers. Numerical results for the shallow shells are also presented and their characteristics are found to be significantly different from the results for the plates.
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Published In
Journal of Engineering Mechanics
Volume 128 • Issue 12 • December 2002
Pages: 1259 - 1266
Copyright
Copyright © 2002 American Society of Civil Engineers.
History
Received: Sep 8, 1999
Accepted: May 23, 2002
Published online: Nov 15, 2002
Published in print: Dec 2002
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